Qualitatively Stable Nonstandard Finite Difference Scheme for Numerical Solution of the Nonlinear Black–Scholes Equation
In this paper, we use a numerical method for solving the nonlinear Black–Scholes partial differential equation of the European option under transaction costs, which is based on the nonstandard discretization of the spatial derivatives. The proposed scheme, in addition to the unconditional positivity...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6679484 |
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| author | Mohammad Mehdizadeh Khalsaraei Ali Shokri Zahra Mohammadnia Hamid Mohammad Sedighi |
| author_facet | Mohammad Mehdizadeh Khalsaraei Ali Shokri Zahra Mohammadnia Hamid Mohammad Sedighi |
| author_sort | Mohammad Mehdizadeh Khalsaraei |
| collection | DOAJ |
| description | In this paper, we use a numerical method for solving the nonlinear Black–Scholes partial differential equation of the European option under transaction costs, which is based on the nonstandard discretization of the spatial derivatives. The proposed scheme, in addition to the unconditional positivity, is stable, consistent, and monotone. In order to illustrate the efficiency of the new method, numerical results have been performed by four models. |
| format | Article |
| id | doaj-art-a4c8f2daa2a146798c67aac38481314f |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-a4c8f2daa2a146798c67aac38481314f2025-02-03T06:06:28ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66794846679484Qualitatively Stable Nonstandard Finite Difference Scheme for Numerical Solution of the Nonlinear Black–Scholes EquationMohammad Mehdizadeh Khalsaraei0Ali Shokri1Zahra Mohammadnia2Hamid Mohammad Sedighi3Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, IranDepartment of Mathematics, Faculty of Science, University of Maragheh, Maragheh, IranDepartment of Mathematics, Faculty of Science, University of Maragheh, Maragheh, IranMechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, P.O. Box 61357-43337, IranIn this paper, we use a numerical method for solving the nonlinear Black–Scholes partial differential equation of the European option under transaction costs, which is based on the nonstandard discretization of the spatial derivatives. The proposed scheme, in addition to the unconditional positivity, is stable, consistent, and monotone. In order to illustrate the efficiency of the new method, numerical results have been performed by four models.http://dx.doi.org/10.1155/2021/6679484 |
| spellingShingle | Mohammad Mehdizadeh Khalsaraei Ali Shokri Zahra Mohammadnia Hamid Mohammad Sedighi Qualitatively Stable Nonstandard Finite Difference Scheme for Numerical Solution of the Nonlinear Black–Scholes Equation Journal of Mathematics |
| title | Qualitatively Stable Nonstandard Finite Difference Scheme for Numerical Solution of the Nonlinear Black–Scholes Equation |
| title_full | Qualitatively Stable Nonstandard Finite Difference Scheme for Numerical Solution of the Nonlinear Black–Scholes Equation |
| title_fullStr | Qualitatively Stable Nonstandard Finite Difference Scheme for Numerical Solution of the Nonlinear Black–Scholes Equation |
| title_full_unstemmed | Qualitatively Stable Nonstandard Finite Difference Scheme for Numerical Solution of the Nonlinear Black–Scholes Equation |
| title_short | Qualitatively Stable Nonstandard Finite Difference Scheme for Numerical Solution of the Nonlinear Black–Scholes Equation |
| title_sort | qualitatively stable nonstandard finite difference scheme for numerical solution of the nonlinear black scholes equation |
| url | http://dx.doi.org/10.1155/2021/6679484 |
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